Question

Show that ( x + 3 ) is a factor of
x^3 + x^2 - 4x + 6

Answer 1

$\huge{\underline{\underline{\tt{\purple{Answer}}}}}\:$

Given is that . Prove that x + 3 is a factor of polynomial $x^3\:+\:x^2\:-\:4x\:+\:6$

If x + 3 would be a factor of this given polynomial then ,

g (x) = x + 3 = 0

x = -3

Substituting the value -3 of the variable x in the polynomial $x^3\:+\:x^2\:-\:4x\:+\:6$

$\implies\:p(x)\:=\:x^3\:+\:x^2\:-\:4x\:+\:6$

$\implies\:p(x)\:=\:(-3)^3\:+\:(-3)^2\:-\:4(-3)\:+\:6\:=\:0$

$\implies\:p(x)\:=\:-\:27\:+\:9\:+\:12\:+\:6\:=\:0$

$\implies\:p(x)\:=\:-\:27\:+27\:=\:0$

$\implies\:p(x)\:=\:0\:=\:0$

Hence , LHS = RHS

Thus proved that x+ 3 is a factor of the polynomial $x^3\:+\:x^2\:-\:4x\:+\:6$

$\huge\star\:\:{\orange{\underline{\pink{\mathbf{Basics}}}}}$

While solving any question related to polynomial use four-step strategy .

• Simplify both sides if you think it's required

• write the equation in standard form

• Factorise the equation

• Zero - Product Principle or LHS = RHS

Answer 2

Step-by-step explanation:

Given is that . Prove that x + 3 is a factor of polynomial x^3\:+\:x^2\:-\:4x\:+\:6x

3

+x

2

−4x+6

If x + 3 would be a factor of this given polynomial then ,

g (x) = x + 3 = 0

x = -3

Substituting the value -3 of the variable x in the polynomial x^3\:+\:x^2\:-\:4x\:+\:6x

3

+x

2

−4x+6

\implies\:p(x)\:=\:x^3\:+\:x^2\:-\:4x\:+\:6⟹p(x)=x

3

+x

2

−4x+6

\implies\:p(x)\:=\:(-3)^3\:+\:(-3)^2\:-\:4(-3)\:+\:6\:=\:0⟹p(x)=(−3)

3

+(−3)

2

−4(−3)+6=0

\implies\:p(x)\:=\:-\:27\:+\:9\:+\:12\:+\:6\:=\:0⟹p(x)=−27+9+12+6=0

\implies\:p(x)\:=\:-\:27\:+27\:=\:0⟹p(x)=−27+27=0

\implies\:p(x)\:=\:0\:=\:0⟹p(x)=0=0

Hence , LHS = RHS

Thus proved that x+ 3 is a factor of the polynomial x^3\:+\:x^2\:-\:4x\:+\:6x

3

+x

2

−4x+6

\huge\star\:\:{\orange{\underline{\pink{\mathbf{Basics}}}}}⋆

Basics

While solving any question related to polynomial use four-step strategy .

●Simplify both sides if you think it's required

●write the equation in standard form

●Factorise the equation

●Zero - Product Principle or LHS = RHS